Winnie, Sarah and Roshel had a total of 52 beads. The ratio of Sarah's beads to Roshel's beads was at first 6 : 7. After Winnie and Sarah each gave half of their beads away, the 3 children had 33 beads left. How many beads did Winnie and Sarah have at first?
| |
Winnie |
Sarah |
Roshel |
Total |
| Before |
2 p |
6 u |
7 u |
52 |
| Change |
- 1 p |
- 3 u |
|
- 19 |
| After |
1 p |
3 u |
7 u |
33 |
Number of beads that Winnie and Sarah gave away
= 52 - 33
= 19
1 p + 3 u = 19
1 p = 19 - 3 u --- (1)
1 p + 3 u + 7 u = 33
1 p + 10 u = 33
1 p = 33 - 10 u --- (2)
(1) = (2)
19 - 3 u = 33 - 10 u
10 u - 3 u = 33 - 19
7 u = 14
1 u = 14 ÷ 7 = 2
From (1)
1 p = 19 - 3 u
1 p = 19 - 3 x 2
1 p = 19 - 6 = 13
Number of beads that Winnie and Sarah had at first
= 2 p + 6 u
= 2 x 13 + 6 x 2
= 26 + 14
= 40
Answer(s): 40
